Regression Analysis

Finance allah shmoop what is regression analysis Regression and elses

no it's not a therapy session in which your psychiatrist

tries to figure out why you've gone back to using

passive fires It's simply this the process by which a

siri's have different independent variables are compay haired to a

dependent variable to see which might have the greatest effect

on the value of the dependent variable All right Well

okay That's The theory of it anyway But what about

some practical examples Well what are these graphs And what

do they tell us Well let's take pete the pizza

joint guy How does he know what's bringing in customers

Is it his new burrito pizza or the virtual skee

ball machines he put in the back Well we can

use some math here to find an equation Usually a

linear one Linear regression Very fine Mathematic sport That best

matches the pattern in the data Then we can see

how close the points are to that line and that

you know will solve our burrito pizza Steve all conundrum

and help pete manage his business better Well the closer

that data points are to the line the more likely

there's some kind of link between the independent and dependent

variables well it doesn't mean one variable causes another It

just means they're linked somehow Like what about the link

between ice cream sales and drownings Death that's a morbid

connection but see how cloaks the data points are to

that special line So yeah there's absolutely some meaningful link

between ice cream sales and drownings deaths greater ice cream

sales on a given day is always linked to mohr

drowning deaths on that day Why what's the linking factor

Flavor of ice cream of the amount of sugar in

the ice cream Too much in ice cream fat and

crap and stuff accessibility to public swimming pools Well clearly

ice cream isn't some insidious killer drowning people who get

in the water without waiting the records that you know

one hour But there is a link between those two

variables Think about it As it turns out hire isis

scream sales happen on hotter days so heat or sunshine

is the linking factor Mohr people go swimming on hotter

days when more people swim while they're going to be

more drowning possibilities anyway so i scream sales in drowning

Deaths are linked but ice cream sales don't cause drowning

death Got it No causal link there Similarly check out

how the points in this graph are not really close

to the line at all There's no link between your

shoe size and your g p a you know unless

you buy huge shoes build a mini computer that fits

in the extra space in your shoes and use that

to help you you know cheat Don't do that by

the way Always cite shmoop anyway back to pete the

owner of zaza pizza Pete almost has more customers lately

than he can handle while the lightning is striking Pete

wants to find a way Teo you know bottle it

The thing is he's made to significant changes to his

restaurant and he's not sure which one is more responsible

for the influx of people tossing money of him Is

it the virtual skee ball machines Or is it his

new burrito pizza Is there in fact any link at

all Well it could be both that are responsible but

that's beyond pete skill and this course to determine he

can only compare one at a time to the increased

Revenue so pete picks different days and plots the number

of burrito pizza orders against the total money made that

day Notice how the data points seem closely to follow

an imaginary line there fromthe lower left to the upper

right In general we can see that low burrito pizza

order numbers are paired with lower daily revenues Also hi

burrito pizza orders are paired with higher daily revenues high

against high low against low will the closer the points

are too that imaginary line the more likely it is

that the independent variable in this case burrito pizza sales

is at least related in some meaningful way to the

dependent variable like it's the pendant on sales of total

daily revenue under our tea i eighty for their or

phone or computer or whatever you're using first week pop

up our data into the list by pressing the stat

button Then enter we put in the ex data in

list one there l won and the y data enlist

to l two Now we press the second key and

the mod key to get out of that menu If

we don't get out of that menu well we're just

begging to screw the pooch here so get out Get

out now we bash stat move over to the cal

commend you and choose option for which is lean wreg

a x plus be all right That's in texas shorthand

for linear regression Yeah on the menu it brings up

moved down to calculator and then press enter if you're

cal doesn't show the r squared and our values Well

you need to hit youtube in search for how to

turn on stat diagnostics t i eighty four there's a

bunch of important info in the results that we need

to check out most importantly for pete's sake is the

value of our the closer that our value is toe

one or negative one The closer the points are two

best fit that possible line Well the closer they are

value is toe one for graphs with positive slopes or

negative one for graphs with negative slope the stronger the

link between the independent independent variables there right That link

is called a correlation right They correlate it doesn't mean

higher daily revenues are absolutely caused by burrito pizza lovers

but it does suggest there somehow correlated and that correlation

is strong anyway The a and b values that you

see on the display happen to be the slope And

why intercept of the equation in the best possible line

pete can use these to predict daily revenues if he

knows the number of burrito pizza sails in a day

But that's a different video Pete still needs to know

if virtual skee ball is so exciting that it might

be more responsible for daily revenue jumps He also plotted

the number of times virtual skee ball was played in

a day versus those same daily revenue figures Well guess

what The points look like a cloud instead of having

any obvious linear pattern Well if we pop that data

into the cal can run the same linear regression process

again we get a very different our value We can

also just see that the points aren't that close to

the line that our value is not close toe one

at all In fact it's cozying up to zero like

it's Ah you know frat boy and zero is well

every girl within a forty meter radius when they are

value is sniffing around zero like that Well it means

there's some kind of very weak correlation between the independent

and deep and it variables We can't stress enough that

this is in proof of any kind of cause no

matter how weak between the two variables just that some

kind of correlation exists and that it's weak pete has

some evidence that the increase daily revenue is almost all

about the burrito pizza and only a tiny bit due

to the virtual skee ball crowd But this is a

big but pete does not have proof they are Value

just suggests that there's some kind of link between the

two variables Not that a change in one variable causes

a change in the other Still with that significant of

a difference in our values pete is pretty safe in

thinking burrito pizza is probably more important in driving higher

revenues than virtual skee ball Pete used a regression analysis

on the two different variables he thought might influence his

bank account the most any decisions he makes killing forward

should probably be menu focused as opposed to you know

attraction focused and still he can't forget the virtual skee

ball entirely It is probably a teeny bit responsible for

the increased mullah in pete's case the correlation between the

variables was positive which means that as burrito pizza sales

or virtual skee ball plays increase well so does daily

revenue there also negative correlations here is well where as

one variable increases the other variable decreases Case in point

carla's customs right next to pete's place carla has customs

takes broken down golf carts and file suits them up

They recently made three distinct changes to their builds and

have noticed a huge decrease in the time it takes

one of their cards to complete the forty r dash

will car lot I wanted to figure out which change

might have been the most responsible for the decreased time's

Carlota plotted forty yard dash times versus the size of

the rims that these things right here they're diameter and

got an r value of negative point one seven nine

when she ran a linear regression of the data then

forty yard dash times versus the cylinder diameter there and

got in our value of negative point six to eight

when she ran a linear regression of that data then

the forty yard dash times versus the nitrous oxide concentration

Is what she ran and she got in our value

of negative point nine four eight when she ran a

linear regression of the data Well guess what The simple

fact here all three plots have some kind of linear

relationship It does mean that there's some kind of correlation

between each of these three variables rim size cylinder diameter

and nitrous oxide concentration you know in the forty yard

dash time of the golf carts with her mostly electric

But we won't get technicals here since all the grafts

have negative slopes and the correlation with nitrous oxide is

the close to the values to negative one The nitrous

oxide concentration has the strongest correlation to decrease forty yard

dash times like it's bad for speed reduced nitrous oxide

in your golf cart it's important to remember that carlotta

can't say that the nitrous oxide concentration is the direct

cause of the faster times All she knows is that

there's a link or a correlation between them Still with

further experimentation carlota could establish a causal relationship Carlotta explored

the relationship between three different variables and their possible effect

on the time to run the forty yard dash using

regression analysis She determined all three variables had some kind

of negative correlation of the times To run the course

as the nitrous concentration or the rim sides or the

cylinder diameter increased well the forty yard dash times decreased

Clearly the nitrous concentration had the strongest correlation Carla should

probably focus on that concentration for the greatest decrease in

times She knows she can't ignore the rim size nor

can she ignore the cylinder diameter as they all contribute

Toe overall Golf cart forty r dash speed times Right

regression analysis will never tell us which variable is the

actual cause It just kind of gives us it's along

the way it's best to make decisions informed by all

the variables that are correlated to the dependent variable And

as kelly clarkson famously saying you know this independent variable 00:10:13.231 --> [endTime] something like that miss independent variable